(Phys.org) —The size of an object can be measured in many ways, such as by its mass, volume, or even the number of atoms it contains. And when it comes to quantum physics, "macroscopic" objects are considered to be larger than "quantum" ones, since the former are usually described by classical laws and the latter by quantum laws. However, physicists have been challenging the boundary between these two realms by performing experiments that show that multiparticle objects can exist in quantum superpositions. But there has been no standard measure of macroscopicity until now, as a team of physicists has proposed that the macroscopicity of an object can be measured in terms of certain parameters of the experiment used to probe its quantum superposition, rather than as a single property of the object itself.

Physicists Stefan Nimmrichter of the University of Vienna, Austria, and Klaus Hornberger of the University of Duisburg-Essen, Germany, have published a paper on the new definition of macroscopicity in a recent issue of *Physical Review Letters*.

In the past, researchers have often measured an object's macroscopicity in terms of the number of atoms in the object. But different atoms are different sizes since they contain different numbers of subatomic particles, which raises the question of whether macroscopicity should be measured in terms of the total number of an object's protons, neutrons, and electrons, or even some other way entirely. As physicists continue to observe quantum effects such as superposition in larger objects, a standard measurement of macroscopicity is needed for comparing these results.

Rather than defining macroscopicity solely in terms of an object's composition, Nimmrichter and Hornberger's definition is based on the idea that quantum equations can be modified to make an object's state more classical. If an experiment can rule out some of these modifications, then it describes a larger quantum superposition and a more macroscopic object. The more modifications an experiment rules out, the more macroscopic the object is.

Several factors can help rule out modifications to achieve a large macroscopicity. For example, a superposition with a long coherence time and an object with a large mass both rule out modifications, among other factors. Taken together, all of these parameters yield a single number, μ, on a logarithmic scale that can be used to grade macroscopicity. On this scale, the superposition state of an object has the same macroscopicity as that of a single electron existing in a superposition for 10^{μ} seconds.

Based on this criteria, the physicists gave scores to some recent superposition experiments. The macroscopicity record score so far is 12, which was achieved by Nimmrichter, Hornberger, and their colleagues in 2010 with a molecule containing 356 atoms. The scientists estimate that atomic clusters containing half a million gold atoms could score a 23 on the macroscopic scale, a feat that would be challenging but not out of reach of future technology.

And what would Schrödinger's cat score on the new macroscopicity scale? The physicists calculated that a 4-kg cat, when in a quantum superposition where it sits in two positions spaced 10 cm apart for 1 second, would score a 57. Knowing this number won't make realizing it any easier, though. The physicists explain that this situation is equivalent to an electron existing in a superposition for 10^{57} seconds, which is about 10^{39} times the age of the universe.

**Explore further:**
Schrodinger's Cat Experiment Proposed

**More information:**
Stefan Nimmrichter and Klaus Hornberger. "Macroscopicity of Mechanical Quantum Superposition States." *Physical Review Letters*. DOI: 10.1103/PhysRevLett.110.160403

Also at arXiv:1205.3447 [quant-ph]

## EyeNStein

## dan42day

## StarGazer2011

## EyeNStein

We think of relativity in smoothly continuous equations but particles with discrete properties.

@ StarGazer's question is the important one on understanding the nature of reality though: As discrete particles simultaneously exist as distributed wavefunctions. We don't have a mathematics to encompass both 'co-states' simultaneously yet. So gravity/relativity and QED smell incompatible at present.

## johanfprins

"Discrete particles" cannot exist simultaneously as distributed waves: If an entity diffracts it MUST be a wave and nothing else but a wave! There are no "particles" .

You are correct to state that gravity/relativity is incompatible with QED. This is so, and will ALWAYS be so since QED is NOT physics but Voodoo. Gravity/relativity blends smoothly with Schroedinger's wave equation, since the latter wave equation is already a relativistic equation.

In fact, even Bohr's quantum-rule for electrons around a nucleus is determined by Einstein's Special Theory of Relativity! When this rule applies for an electron circling a nucleus, the electron must form a stationary Schroedinger wave.

## EyeNStein

Physics would be a lot easier (and the physical world a lot stranger) if everything were only wavefunctions. And Dirac did indeed bring wavefunctions and relativity together: But that became the root of the 'standard model' of Quantum theory. The fact that these spread out wavefunctions co-manifest as the various bosons and fermion particles in localised space is well demonstrated and quantified at this point in time.

If you have a set of equations to unify these two co-states simultaneously there is a nobel prize waiting for you.

## johanfprins

Not wavefunctions but actual electromagnetic waves which can all be derived from Maxwell's equations.

No he did not! He "derived" an incorrect wave equation for a SINGLE electron and when he solved it he found that the electron must end up having an energy of MINUS infinity.

No it is NOT!

I have the equations: I only hope that I live long enough to break through the bigotry and get the Nobel Prize! BTW, I should already have received this prize 13 years ago when I PROVED that superconduction can occur up to 400 C.

## EyeNStein

The Wavefunction is a root probability distribution function which co-exists with (or collapses to produce) particle like behaviour which locallises their interactions. Which is what we will call particles, at least until we understand Heizenberg better.

You will need to unify the strong force and gravity with the electroweak force and derive the various 'particle forms' to get your Nobel.

## johanfprins

How did this "go out" with de Broglie? The de Broglie wavelength is caused by the Lorentz transformation; where the latter results from Maxwell's equations.

No it is NOT a probability distribution: It is the electric-field potential of the EM-wave which IS the electron.

What you call a "particle" is a localized EM-wave: It is always a wave! Heisenberg believed in Voodoo.

I do NOT need to derive "particle forms" since there are no "particles" whatsoever!

## johanfprins

The gravity-field is the "tunneling tails" of the matter waves, which have NOTHING to do with tunneling. Tunneling, as modeled within the mainstream literature, is impossible since it requires negative kinetic-energy. What is called "tunneling" occurs by the borrowing of energy (so called "zero-point" energy, or "vacuum-energy" as advocated by the morons) for an allowed time (delta)E in order to SCALE a potential barrier: NOT to move through it: The latter violates the conservation of energy!

## Disproselyte

This transition is relative, depending on the state of the considered system and well understood in the framework of scale relativity: e.g.: http://luth2.obsp...irac.pdf

## johanfprins

I have noted this interesting paper before. It is, however, based on Minkowski's "space-time" which does not exist since x,y,z, and t are not linearly independent coordinates as they must be to define unique space-time distances s between any two space-time points like (x,y,z,t) and (x(p),y(p),z(p),t(p)).

Minkowski's "space-time" violates the rules of mathematics which require that there can be only one point (at the origin) within such a "space-time" for which x=0, y=0, z=0, and t=0. In Minkowski "space-time" there are many such points other than the origin, thus making it impossible to have unique distances s between space-time points.

## EyeNStein

So presumably you don't believe in special relativity either??

Without Minkowski space-time how do you generate invariant space-time displacements?

Its our naturally perceived universal time which doesn't exist, and doesn't let you define a single invariant origin point for all observers in all frames.

## johanfprins

I have no stated that I do not believe in the Lorentz-transformation!

You do not; since they do not exist!

All clocks no matter in which inertial reference frame they are and no matter with which velocities they move relative to one another show EXACTLY the same time at ANY instant in time. When you transform an event from an inertial reference frame into another IRF the transformed difference in time is NOT simultaneously displayed on the clocks but are two different times, where each of these times register simultaneously on all the clocks within gravity-free space. If this is not the case the relative speed of light will not be c within all IRF's.

## johanfprins

The equations of the Lorentz-transformation are derived by assuming that a laser-source emits a unidirectional wave-front from the position in space where and when the origins of two inertial reference-frames IRF=K and IRF=K/, moving with a speed v relative to one another, coincide. It is found that the physics when the light-source is stationary within IRF=K/ only allows a Lorentz-transformation from IRF=K/ to IRF=K: Not the reverse transformation from IRF=K into IRF=K/. Similarly, it is found that the physics when the light-source is stationary within IRF=K, only allows a Lorentz-transformation from IRF=K into IRF=K/: Not the reverse transformation from IRF=K/ into IRF=K. For this reason, contrary to accepted dogma, the clocks within IRF=K and IRF=K/ must keep time at exactly the same rate.

## EyeNStein

The relative speed of light will always be c within all IRF's. Regardless of the light source IRF or the IRF it is viewed/measured from.

As for MST 'not existing'; as it is a valid mathematical abstraction to create Space-Time displacement invariance: Whether it physically exists is open for debate at 2am in a student bar. Meanwhile MST is a useful concept even if it did give us E=MC2 and indirectly the atomic bomb.

## johanfprins

Where have I stated otherwise?

Epicycles were a "valid mathematical abstraction" but are not physics. MST is not even a "valid mathematical abstraction"!

Where did MST give us E=mc^2? Mass being energy has NOTHING to do with the validity of MST. MST is not physics nor mathematics at all. It is amazing that Minkowski, who was a professor in mathematics, could postulate a space-time by equating two expressions which are separately and independently equal to zero, and then claim that they are connected by a unique space-time distance! Insanity?

## Whydening Gyre

## EyeNStein

E=mc^2 derives in Minkowski space-time by simply rearranging the expressions for momentum and kinetic energy in that space. That is where the expression for relativistic increased mass of a (fast) moving object comes from too.

These physical effects are demonstrated by experiments. Supporting their derivations.

## johanfprins

E=m*c^2 can be derived simply and directly from Newton's laws by the assumption that moving mass energy is different from stationary mass-energy. Why use Minkowski space which violates the mathematics of linear spaces so that there cannot be invariant four-dimensional space-time distances within Minkowski space?

## EyeNStein

## johanfprins

I disagree! As far as Special relativity is concerned we do live in linear spaces with absolute time, just as Newton has assumed. The only difference is that an event that occurs within a linear space which moves with a speed v relative to you is observed relative to the origin of your linear space at a non-coincident time and a non-coincident position. This can be derived from the Lorentz transformation: See: http://www.cathod...tion.pdf

The problem is that MST violates the rules of mathematics since it claims that x,y,z,and t are linearly independent coordinates while they are not; as you will see when reading my manuscript quoted above.

## EyeNStein

## johanfprins

This is modeled and explained in detail in the reference I gave you: i.e. within: http://www.cathod...tion.pdf

It is not possible to post the whole derivation here. Please read the document and then ask pertinent questions about the contents of the document.

In short it is not the clock moving with the muon which keeps slower time, but the time at which the muon is generated within its own inertial reference (in which it is stationary) is different from, and does not coincide with the time as measured relative to earth; even though the clock on earth and the clock with the muon keep exactly the same time. It sounds strange but this is what the Lorentz transformation demands when the speed of light is the same within both reference frames.

## EyeNStein

This is an utterly implausible suggestion compared to the Special Relativity principle which asserts that time passes at a slower rate for the muon because of its large velocity.

Your assertion that, balancing two similar space-time equations by equating 0=0 is invalid, would only apply if the dimentionality was mismatched (eg. apples=oranges) but that is not the case here.

## johanfprins

It might sound implausible but this is what the Lorentz transformation demands. Thus if the Lorentz transformation is correct this derivation must be correct.

The muon is stationary relative to its own clock within its own inertial reference frame: Thus according to the principle of relativity this clock cannot keep slower time. The lifetime of the muon within its own IRF does not increase as you claim it does!.

## ValeriaT

## ValeriaT

## johanfprins

You know less about physics, mathematics and logic than an ape knows about religion; and you are just as stupid. Please leave physics to people who have brains and real self awareness.

This again illustrates how stupid you are. according to Einstein's first postulate a muon's lifetime must be exactly the same within ANY IRF within which it is stationary. The muon approaching the earth is stationary within its own inertial reference frame so that a clock travelling with it CANNOT keep slower time.

Please stop thinking you can play in the big league: You are just too stupid!

## ValeriaT

## johanfprins

I know it actually is and must be

You do not need your dense aether model to understand it.

Please save me another embarrassing display of your stupidity.

There is NO NEW information or logic from you! Your AWT is plain bullshit. If you want to prove that it is not so, fit your equations to actual data instead of making silly cartoons which can fit any hallucination of any demented mind!

## EyeNStein

This slanging match isn't advancing our understanding of the universe we find ourselves in.

Relativity and Quantum Electrodynamics currently rule as theories of 'how stuff happens'. They fit the data/facts and have passed each test applied in the search for any new (inconsistent) physics such as you guys keep dreaming up. The only inconsistencies I've seen are coming out of our heads: Where facts contradict theories, no matter how beautiful or cherished, no matter how many papers or letters after your names - such theories are wrong. No matter how many ways you find to look sideways with one eye closed at the data.

If your theories are any good they must predict a RESULT which current theory cannot explain.

## johanfprins

A very naive way to look at physics, In the time of Galileo epicycles explained the motion of planets as seen from the earth equally well as the Copernicum system explained them; but epicycles were wrong physics. In fact the same silly argument you have just now posted were then used against Galileo. The Copernicum model cannot predict a result that the epicycles cannot explain.

It is well known in physics that you can get different models which model the same data. Which one is correct? Friar Ockham suggested that the simplest of these models is usually correct.

The equations on which STR is based (Lorentz transformation) is at present accepted by all to be correct. But the results derived from it can be interpreted in different ways: For example, the "time dilation" formula can be interpreted as being the simultaneous times on two clocks or different non-simultaneous time on both.

## johanfprins

However, the clocks being flown around the world do NOT move linearly relative to the clock on earth. Furthermore the flying clocks are being accelerated and are flying at different heights through the earth's gravity field. The data had to be "corrected" to get the result that the experimenters wanted to get. There is thus no real direct proof that two clocks moving linearly relative to one another do keep time at different rates. In fact, if they do,.this will violate Einstein's postulates on which he based his Special Theory of Relativity: Since each clock is stationary within its own IRF, each clock MUST have the same time rate within its own IRF.